We investigate the rotational response of both nondipolar and dipolar Bose-Einstein condensates confined in an annular potential via minimization of the energy in the rotating frame. For the nondipolar case we identify certain phases which are associated with different vortex configurations. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms. © 2013 American Physical Society.